Separability of mixed states: necessary and sufficient conditions

  title={Separability of mixed states: necessary and sufficient conditions},
  author={Michal Horodecki and Paweł Horodecki and Ryszard Horodecki},
  journal={Physics Letters A},
Partial separability revisited: Necessary and sufficient criteria
We extend the classification of mixed states of quantum systems composed of arbitrary numbers of subsystems of arbitrary dimensions. This extended classification is complete in the sense of partial
Separability Properties of Three-mode Gaussian States
We derive a necessary and sufficient condition for the separability of tripartite three-mode Gaussian states that is easy to check for any such state. We give a classification of the separability
Separability criteria based on the bloch representation of density matrices
The necessary condition is proved to be strong enough to detect bound entangled states and the proofs of the sufficient conditions are constructive, thus providing decompositions in pure product states for the states that satisfy them.
Some necessary and sufficient conditions for k-separability of multipartite pure states
A necessary and sufficient condition for k-separability of pure states in any multipartite quantum systems of finite or infinite dimension is given.
Sufficient and necessary conditions of separability for bipartite pure states in infinite-dimensional systems
The PHC criterion and the realignment criterion for pure states in infinite-dimensional bipartite quantum systems are given. Furthermore, several equivalent conditions for pure states to be separable
Generalized Circulant Densities and a Sufficient Condition for Separability
In a series of papers with Kossakowski, the first author has examined properties of densities for which the positive partial transpose (PPT) property can be readily checked. These densities were also


Information-theoretic aspects of inseparability of mixed states.
  • Horodecki
  • Psychology
    Physical review. A, Atomic, molecular, and optical physics
  • 1996
Information-theoretic aspects of quantum inseparability of mixed states are investigated in terms of the {alpha} entropy inequalities and teleportation fidelity and a complete characterization of the inseparable 2{times}2 systems with maximally disordered subsystems is presented within the Hilbert-Schmidt space formalism.
Bell's Inequalities and Density Matrices: Revealing "Hidden" Nonlocality.
  • Popescu
  • Physics
    Physical review letters
  • 1995
For mixed states, correlations arising from a single ideal measurement on each system may obey standard Bell inequalities, yet when each system is subjected to a sequence of ideal measurements the correlations are nonlocal.
Bell's inequalities versus teleportation: What is nonlocality?
  • Popescu
  • Physics
    Physical review letters
  • 1994
The nonlocality responsible for violations of Bell's inequalities is not equivalent to that used in teleportation, although they probably are two aspects of the same physical property. There are